To determine if the expressions [tex]\(2(x+3)\)[/tex] and [tex]\(2x+4+2x\)[/tex] are equivalent when [tex]\(x=2\)[/tex], we need to evaluate the second expression [tex]\(2x+4+2x\)[/tex]:
1. Start with the given value of [tex]\(x = 2\)[/tex].
2. Substitute [tex]\(x = 2\)[/tex] into the second expression:
[tex]\[
2x + 4 + 2x = 2(2) + 4 + 2(2)
\][/tex]
3. Perform the multiplications first:
[tex]\[
2(2) + 4 + 2(2) = 4 + 4 + 4 = 4 + 4 + 4
\][/tex]
4. Add the terms together:
[tex]\[
4 + 4 + 4 = 12
\][/tex]
Now we need to compare this result to the value of the first expression [tex]\(2(x+3)\)[/tex] when [tex]\(x=2\)[/tex]:
1. Substitute [tex]\(x = 2\)[/tex] into the first expression:
[tex]\[
2(x+3) = 2(2+3) = 2(5) = 10
\][/tex]
Because the value of the second expression is 12 and the value of the first expression is 10, the two expressions are not equivalent.
Thus, the correct option is:
- The value of the second expression is 12, so the expressions are not equivalent.
